Philosophy Of Physics
@PhilosophyOfPhy • 125,583 subscribers
Study physics. Not for formulas, but for the thinking process.
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The rocket’s fins emerge from motions that extend around the whole curve. Each Fourier harmonic contributes a repeating oscillation; even a small corner takes many frequencies working together. One rotating chain reconstructs the horizontal coordinate, the other the vertical. Their guides meet at the pen. As the count rises from 1 to 100 harmonics per coordinate, an ellipse becomes an increasingly accurate rocket outline.
Philosophy Of Physics312,630 次观看 • 6 天前
Sharp feather tips can be approximated by adding smooth sine and cosine waves. This hummingbird’s outline is described by two Fourier series, one for each coordinate. Their rotating chains position the pen where the horizontal and vertical guides meet. Low frequencies capture the broad shape; higher frequencies recover smaller details. The number below the bird is the highest harmonic retained in each coordinate. At 100, the largest sampled pointwise error is about 0.57% of the outline’s height.
Philosophy Of Physics37,965 次观看 • 5 天前
Each rotating circle contributes to the whole seahorse. Its outline is encoded in two Fourier series, one for the horizontal coordinate and one for the vertical. The guides from the two chains meet at the moving pen. With one harmonic per coordinate, the trace is an ellipse. Adding harmonics brings out the snout, jagged back and curled tail. At 100 harmonics per coordinate, the largest sampled pointwise error is about 0.45% of the outline’s height.
Philosophy Of Physics34,484 次观看 • 6 天前
A quantum system can complete a cycle and return to its original physical state, yet retain a measurable trace of the journey. During slow, cyclic evolution, its wavefunction can acquire an additional phase that depends on the path taken through parameter space. This is the Berry phase. For a spin-½ system, the geometric phase is related to the solid angle enclosed by the path on the Bloch sphere, γ = −Ω/2. Its deeper significance is that quantum evolution can retain information about the geometry of a path, even after the system returns to its starting point.
Philosophy Of Physics34,404 次观看 • 8 天前
A jet at Mach 1.5 passes 1.5 km over your head and you hear nothing. It is already past you before any of its sound arrives. Then, 3.3 s after it went overhead, the cone of its own sound reaches you: the boom. The jet outruns its own noise. Its wavefronts pile up into a cone with sin μ = 1/M, here μ = 41.8°, which meets you at t = h√(M²−1)/(Mc). After that, every moment brings sound from two points on the flight path. One plays forward, slowed toward 0.4× speed. The other was sent while the jet was still approaching, and it arrives in reverse order at nearly 2× speed. So for a while you hear the jet's past running backwards. These are exact arrival times for a point source in still air at 343 m/s. The model engine ticks every 0.5 s so you can hear the order, and the jet is drawn far larger than life.
Philosophy Of Physics21,696 次观看 • 6 天前
After reentering Earth's atmosphere at hypersonic speed, the Space Shuttle had no engines to help it land. Once it dropped out of orbit, it became a heavy glider, relying only on gravity, aerodynamics, and the pilot's precision. There were no second chances. The shuttle had a steep descent, a narrow landing window, and just one shot at the runway.
Philosophy Of Physics448,963 次观看 • 8 个月前
Each coordinate of a closed butterfly outline has its own real Fourier series: x(t) = Σₖ (aₖ cos kt + bₖ sin kt), and similarly for y. A sine–cosine pair at frequency k corresponds to an arm of length √(aₖ² + bₖ²), turning k times per lap. One chain sets x, another sets y, and the pen sits where their guides cross. With N harmonics per axis, the maximum sampled reconstruction error is 30.45% of the butterfly’s height at N = 1, 1.15% at N = 50, and 0.52% at N = 100. At N = 1, both coordinates are pure sinusoids: an ellipse. The higher harmonics recover the wings and narrow body, turning that ellipse into a butterfly.
Philosophy Of Physics17,940 次观看 • 7 天前
![In 1926, Erwin Schrödinger introduced the equation that became the dynamical law of non-relativistic quantum mechanics: iℏ ∂ψ/∂t = [−ℏ²/(2m)∇² + V]ψ It does not describe a particle following one definite path. It describes how the wavefunction evolves and therefore how the probabilities of possible experimental outcomes change with time.](https://image.24vids.com/tw-2079986079629967480/amplify_video_thumb/2079957991642861569/img/8A3f_Zn1DuI0a1Rb.jpg)
In 1926, Erwin Schrödinger introduced the equation that became the dynamical law of non-relativistic quantum mechanics: iℏ ∂ψ/∂t = [−ℏ²/(2m)∇² + V]ψ It does not describe a particle following one definite path. It describes how the wavefunction evolves and therefore how the probabilities of possible experimental outcomes change with time.
Philosophy Of Physics126,180 次观看 • 2 个月前
What looks purely electric to one observer can contain a magnetic field for another. Changing the observer’s motion changes how the same electromagnetic field is divided into electric and magnetic components. The field tensor reveals the deeper structure: electric and magnetic fields are parts of a single electromagnetic field. Observers may disagree about E and B separately, while specific combinations of them remain invariant.
Philosophy Of Physics17,899 次观看 • 9 天前
You cannot detect spacetime curvature by watching a single freely falling object. Locally, it simply follows its natural path through spacetime. The curvature becomes visible when we compare neighboring free-fall trajectories. Their separation can grow or shrink even when no ordinary force acts between them. This relative acceleration, geodesic deviation,is what we experience as tidal gravity, revealing gravity as a property of spacetime geometry itself.
Philosophy Of Physics26,179 次观看 • 16 天前
